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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 107, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.107 (Mi sigma1644) 		 
Quasi-Invariants in Characteristic $p$ and Twisted Quasi-Invariants

Michael Rena, Xiaomeng Xub

a Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
b School of Mathematical Sciences and Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
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DOI: https://doi.org/10.3842/SIGMA.2020.107
Abstract: The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597–611]. Their Hilbert series over fields of characteristic 0 were computed by Feigin and Veselov [Int. Math. Res. Not. 2002 (2002), 521–545]. In this paper, we show some partial results and make two conjectures on the Hilbert series of these spaces over fields of positive characteristic. On the other hand, Braverman, Etingof and Finkelberg [arXiv:1611.10216] introduced the spaces of quasi-invariant polynomials twisted by a monomial. We extend some of their results to the spaces twisted by a smooth function.
Keywords: quasi-invariant polynomials, twisted quasi-invariants.
Funding agency
We would like to thank MIT PRIMES, specifically Pavel Etingof, for suggesting the project.
Received: July 10, 2020; in final form October 17, 2020; Published online October 27, 2020
Bibliographic databases:
Document Type: Article
MSC: 81R12, 20C08
Language: English
Citation: Michael Ren, Xiaomeng Xu, “Quasi-Invariants in Characteristic $p$ and Twisted Quasi-Invariants”, SIGMA, 16 (2020), 107, 13 pp.
Citation in format AMSBIB
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